The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions

Oliver Linton, Enno Mammen and J. Nielsen
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J. Nielsen: PFA Pension

No 1160, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We derive the asymptotic distribution of a new backfitting procedure for estimating the closest additive approximation to a nonparametric regression function. The procedure employs a recent projection interpretation of popular kernel estimators provided by Mammen et al. (1997), and the asymptotic theory of our estimators is derived using the theory of additive projections reviewed in Bickel et al. (1995). Our procedure achieves the same bias and variance as the oracle estimator based on knowing the other components, and in this sense improves on the method analyzed in Opsomer and Ruppert (1997). We provide 'high level' conditions independent of the sampling scheme. We then verify that these conditions are satisfied in a time series autoregression under weak conditions.

Keywords: Additive models; alternating projections; backfitting; kernel smoothing; local polynomials; nonparametric regression (search for similar items in EconPapers)
Pages: 39 pages
Date: 1997-09
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Citations: View citations in EconPapers (16)

Published in The Annals of Statistics (1999), 27: 1443-1490

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Related works:
Working Paper: The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions (2000)
Working Paper: The existence and asymptotic properties of a backfitting projection algorithm under weak conditions (2000)
Working Paper: The existence and asymptotic properties of a backfitting projection algorithm under weak conditions (1999)
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